exercices corrigés value at risk


Comment calculer la valeur ajustée au risque ?

  • 3.2. La Value-at-Risk (VaR) La notion de Value-at-Riskou valeur ajustée au risque s’est originellement développée dans les milieux financiers avant d’être largement reprise dans les problématiques assurantielles. Définition 5 : La Value-at-Risk (VaR) de niveau ?associée au risque X est donnée par : VaR()X,?=Inf{}xPr[X?x]??.

Comment calculer la Value-at-Risk ?

  • Définition 5 : La Value-at-Risk (VaR) de niveau ?associée au risque X est donnée par : VaR()X,?=Inf{}xPr[X?x]??. On notera que VaR()?=?1(? où désigne la fonction quantile de la loi de X.

Comment calculer la valeur en risque ?

  • Il estdonc normal que la valeur en risque soit plus petite que celle obtenue avec l’approximationgaussienne (car on rappelle que l’excès de kurtosis est très faible). En utilisant un historique de rendement, on peut calculer la valeur du PnL avec la formule précédenteen remplaçantRt+1par les scénarios historiques.

Comment définir la relation de risque ?

  • ? Définition 13 : Pour toute mesure de risque ?, pour tous risques X et Y, on définit la relation p?par : Xp?Y si ?()X??(Y) Proposition 15 : La relation issue de la mesure de risque ?est réflexive et transitive. De plus il est toujours possible de comparer par deux lois de probabilité ou deux variables aléatoires.
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